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The theory of electrodynamic space-time relativity (Revision 2)

Yingtao Yang

Toronto, Canada, yangyingtao2012@hotmail.com

Abstract: The theory of electrodynamic space-time relativity (TESTR) is the study of the

transformation of time and space between two electrodynamic inertial frames of reference, which have

both inertial velocity difference and electric potential difference. It is a fundamental space-time theory

of theoretic physics based on the Einstein’s special theory of relativity, the electric potential limit

postulate and the high-precision experimental facts of the inversion proportional square law of

Coulomb’s force. It founded new physical space-time concepts, for example, the electrodynamic space-

time is five-dimensional which is composed of quaternion space, and time. It also proposed some new

basic concepts of physics, such as electric potential limit, quaternion electric potential and etc., revealing

the inherent relationships between electric potential-velocity and time-space. This paper discusses in

detail the process of establishing the theory of complex electrodynamic space-time relativity and theory

of quaternion electrodynamic space-time relativity as well as their various conversions and

transformations. At the same time, the basic effects of TESTR were discussed, obtaining the equations

for superposition of quaternion velocity and potential of TESTR. It predicts some important new space-

time change effects, which provides theoretical basis for the experimental validation of TESTR. This is

the fundamental theory of the author’s series.

Keyword: theory of electrodynamic space-time relativity, theory of complex electrodynamic

space-time relativity, theory of quaternion electrodynamic space-time relativity, theory of electric

potential relativity, special theory of relativity, electric potential limit, complex speed, complex electric

potential, quaternion velocity, quaternion electric potential, quaternion, electrodynamic space-time, five-

dimensional space-time, the time expansion effect of electric potential, electrodynamic space-time

effects

The two pillars of modern physics are quantum mechanics and the theory of relativity which were

both proven through numerous experiments. However, on the fundamental understandings, such as the

“actuality” of physics, there are profound contradictions between quantum mechanics and general

relativity. For the past century, many attempts to unite quantum mechanics and general relativity have

been unsuccessful. At the same time, problems such as dark matters and dark energy also cannot be

explained by current theories, revealing flaws in the current fundamental theory of physics.

It is well-known that the Dirac equation of quantum mechanics was built upon the relationship

between energy and momentum of the special theory of relativity (STR). The general theory of

relativity was also developed through advancement of the basic postulates of the STR. If there are

unsolvable conflicts between quantum mechanics and general relativity, the root cause may be related to

special theory of relativity. However, STR has been well proven through abundant experiments, and its

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correctness is sufficiently confirmed. Hence one cannot help but to doubt the completeness of special

theory of relativity. In another word, our current understanding of time, space, and momentum may not

be complete. To discover what the “incompleteness” of STR is, and to establish more complete space-

time relativity, are of great significance for deepening our understanding on the basic physical concepts

such as space-time, matter and motion. This will solve a series of basic problems in current physics and

accelerate developments of physics.

Part 1. The theory of complex electrodynamic space-time relativity (TCESTR)

Einstein’s special theory of relativity is based on two basic postulates [1]

about inertial motion, that

is:

1. The principle of relativity: physical laws should be the same in every inertial frame of reference

2. The principle of invariant speed of light: in any inertial system, the speed of light in vacuum is a

constant.

According to these two postulates, the famous Lorentz transform equations can be derived.

( ) (1)

(2)

(3)

(

) (4)

√

(5)

Here, the Lorentz transformation equations are scalar equations, where is the speed along x-axis

of inertial frame ( ) relative to the inertial frame ( ). is the speed of light.

and are the length and time of the observing system and the observed system,

respectively.

Upon analyzing the basic postulates of the special theory of relativity, a question can be asked: is

our understanding of motion complete? Is there another physical reference frame besides the inertial

reference frame, where the same the physical laws still hold in each frame of reference when it is under

different states? In this physical reference frame, the state of such reference frame cannot be determined

through any experiment. Does the related physical parameters have limit? And would such limit lead to

the relativistic effect of time and space? After further study, it was found that equipotential bodies are of

such physical reference systems. Based on Coulomb's inverse proportional square law and its high-

precision experiments [2]

, we know that within a closed conductor of any shape, the electric potential at

any point is the same regardless of how much electric charge its surface carries. In addition, the interior

electric field strength E is zero. This is a corollary of Gauss' law of electric field.

Thus, a thought experiment can be carried out: there are two identical closed metal carriages A and

B, and they are motionless relative to each other and are insulated from each other with only carriage B

being grounded. Suppose there is an electrode of an ultra-high voltage static electric generator

connected to B, and the other electrode is connected to the carriage A. Let the electric potential of the

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ground be zero. Once the generator starts running and continues to charge the carriage A with

electrical charges (either positive or negative), the electric potential on the surface and in the interior of

the carriage increases with it. When the surface electric charges reach Q, the interior and surface

electric potential is the same everywhere. At the same time, the electric field intensity is zero.

Therefore, when an observer is isolated inside carriage A, it is impossible for the observer to know the

values of electric potential or whether it is positive or negative relative to carriage B through any

experiment. Same can be said for the observer in the carriage B where the electric potential is zero,

even when there is a very high electric potential difference between them. Please note that same

experimental results can be obtained in the inertial frames of reference. Therefore, we can put forth

two postulates of equipotential reference system:

3. Relative principle of electric potential: physical law has the same form in any electric

equipotential frame of reference;

4. Postulate of electric potential limit: in any equipotential frame of reference, electric potential

limit is a constant at any point in vacuum.

The value for such electric potential limit only can be determined by experiment. Its possible

value could be the Planck voltage which is volts, or of similar magnitude.

There seems to have conflicts between the postulate of electric potential limit and the current

electromagnetism. However, there is not any experiment that proves whether or not electric potential

has limit. In addition, electromagnetic theory is not perfect, as there are difficulties that cannot be

overcome by the current theory itself, such as that the energy of a point charge is infinite. Hence, it is

logical to propose such postulate that electric potential limit.

If the postulate is true, the current Maxwell’s equations must be modified. When electric potential is

far lower than the electric potential limit, the modified Maxwell’s equations will revert back to the

current Maxwell’s equations (this will be discussed in another paper).

Special theory of relativity and the current Maxwell’s equations are covariant. Hence the applicable

conditions of the STR are the same, such that electric potential is much lower than the electric potential

limit. Therefore, the space-time theory of physics must be further developed.

By comparing the relative principle of electric potential and the postulate of electric potential limit

with the two postulates of the special theory of relativity, it can be seen that their forms are very similar.

When the two postulates are established, it leads to the possibility of a new theory of relativity such is

the electric potential relativity. It has symmetric relationship with the STR. Further reasoning will

reveal that both STR and the theory of electric potential relativity are special cases of a higher level

theory of relativity. This higher level relativity theory would be the study of space-time relationship

between two frames of reference with both velocity difference and electric potential difference. In order

to establish such “higher level theory of relativity”, both the electric charge state (electric potential) and

the motion state (speed) of the same frame of reference must be unified. In modern physics, however,

the concepts of electric potential and speed have no direct correlation. Through in-depth study, it was

discovered that in order to solve this contradiction, new physical concepts such as imaginary motion,

complex motion and etc., must be introduced.

To investigate this problem, suppose at random point P in the equipotential space:

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Where is the electric potential limit, is electric potential of point P, and β is the ratio between

the electric potential and the electric potential limit. Even though equipotential frame of reference is

very similar with inertial frame of reference, but the equipotential frame of reference is stationary in the

three-dimensional space. It cannot be defined as a regular inertial reference frame. Equipotential

reference frame will be defined as the inertial frame of reference of the imaginary speed. Because

equipotential space-time and inertial space-time are homogeneous and isotropic, therefore corresponding

relationship exists between electric potential and imaginary speed. The electric potential limit is

equivalent to the imaginary speed of light . The potential is equivalent to the imaginary speed .

From the perspective of complex number, both and are scalar. That is:

Where，imaginary number √ ,

Hence the following formula is established:

(6)

Let， (7)

Here,

, is an imaginary constant, and can be named as the electrodynamic conversion factor.

To further investigate more general space-time relationship, we must extend our concept of motion

and space-time from the real number domain to the complex number domain. The more general motion

can be abstractly understood as the motion state in the complex plane. If the motion in the coordinate

reference system possesses both real and imaginary motion, then we call its motion state the complex

motion state. The frame of reference situated in the complex motion state is called complex inertial

electrodynamic frame of reference; it has both equipotential and inertial motion. The theory to describe

this space-time relation of such motion is called the theory of complex electrodynamic space-time

relativity.

As shown in Figure 1, let there be two complex coordinate systems of reference ( )and

( )in the same complex plane. Their imaginary axis and , real axis and are all parallel

to each other. Since in complex number there is no vector, therefore all the relevant physical parameters

of motion must be scalars quantities such as speed and distance. Let ( ) be the stationary

observing reference frame that is, the imaginary speed is zero (the electric potential is zero) and real

speed is also zero. While ( ) is the observed reference frame and in complex motion state

relative to ( ), its complex speed is , its imaginary speed is and real speed is , and is

the complex angle.

(8)

The modulus of complex speed is: √

(9)

Where,

(10)

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Figure 1

Since real electric potential can be converted into imaginary speed, then by symmetry principle, real

speed can be converted into imaginary electric potential . Therefore,

，where

real electric potential and imaginary electric potential together forms complex electric

potential ：

(11)

The modulus of complex electric potential is:

√ (12)

Where,

(13)

Multiplying both sides of the equation (11) with K, and comparing with equation (8), we get:

(14)

This shows that complex speed and the complex electric potential are inter-convertible. Therefore

the complex reference frame of electric potential is a type of complex electrodynamic inertial reference

frame. To take one step further, the above four basic postulates will be combined into two basic

postulates of TCESTR. Since complex numbers cannot be compared in magnitude, but their modulus

can, hence we have:

5. The principle of the complex electrodynamic space-time relativity: physical law has the same

form in any complex electrodynamic inertial frame of reference;

6. The postulate of complex electrodynamic time-space limit: in any complex electrodynamic

inertial reference system, the limit of complex speed’s modulus of any point in vacuum is a constant, ;

or the limit of complex electric potential’s modulus of any point in vacuum is a constant , .

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Where, is the speed of light in the vacuum with zero electric potential, and is equal to

299,792,458 m/sec. The limit of complex electric potential’s modulus can only be determined by

experiment.

One of the inference can be derived from postulate 6 is that in the frame of reference where electric

potential is not zero, the speed of light in the real three-dimensional space is less than . However,

the complex speed’s modulus of the light in the complex space is . (This is proven in subsequent

paper regarding expansion of the Maxwell’s equations).

When , the two above postulates become the postulates of the theory of electric

potential relativity. When , the two above postulates become the fundamental

postulates of the special theory of relativity. Hence, special theory of relativity and the theory of electric

potential relativity are two special cases of TCESTR.

The special theory of relativity is commonly referred to the motion of the observed system relative

to the observing system along an axis and is called one-dimensional special theory of relativity. In fact,

such motion can have two-dimensional or three-dimensional forms and the corresponding the special

theory of relativity become more intricate but also more universal. There are already detailed

discussions in literatures on this matter, showing that in the real space two-dimensional [3]

and three-

dimensional special theory of relativity [4]

in arbitrary direction can be derived through rotation and

translation of the coordinate system of one-dimensional special theory of relativity; or three-dimensional

special theory of relativity can be derived through vector transformation of one-dimensional special

theory of relativity[5], [6]

. Although they are difference in their derivation methods, there is a common

theme, that is, through the use of one-dimension special theory of relativity and appropriate

mathematical approach, the higher real form of special theory of relativity can be derived. Therefore,

based on the above mentioned postulates and one-dimension special theory of relativity, TCESTR may

be derived by a way of transforming the complex coordinate system.

As shown in Figure 1, let there be a random point P0 be in the complex plane. In different complex

coordinate systems, it can be represented by different coordinate parameters. In the complex coordinate

system ( ), the coordinate of is represented by complex distance with complex

angle is . In the coordinate system ( ), the coordinate of point is represented as complex

distance with complex angle . Refer to method of two dimensional coordinate

transformation of real numbers [3]

, and expanding it into the complex planar space, reference system

( ) can be obtained through three times coordinate transformations from reference system

( ).

(1) In the complex coordinate system ( ), its time is , rotating the coordinate system

by degree counterclockwise, we get complex coordinate system ( ), , whose time

is ;

(2) Complex coordinate system ( ) is translated along axis of real number in the

quantity equal to the modulus of the complex speed | , we get complex coordinate system

( )., whose time is ；

(3) Complex coordinate system ( ). is rotated by degree clockwise, we get

complex coordinate system ( ), whose time is .

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The detailed derivation steps, numbered corresponding to the above, are as follow:

(1) Rotate the coordinate system ( ) by degree counter clockwise, making the real axis

of the coordinate system ( ) pass through the origin of the reference system ( ).

Point P0 in ( ) complex coordinate system has complex distance , whose complex angle is .

Point P0 in the coordinate system ( ) has complex distance , whose complex angle is .

That is,

(15)

(16)

Also, | |，therefore，

（ )

(17)

( )( ) (18)

From equations (18) and (16),

(19)

(20)

(2) Let ( ) be the stationary frame of reference whose time is . ( ) is the

moving reference system whose time is , and real axes and are overlapping. The reference

system ( ) moves along the positive direction relative to ( ) with the

magnitude of | , hence . Since is the real number axis of ( ), it can be thought

as the real motion. This is the same state that the special theory of relativity studies. Hence the Lorentz

transform equations (1), (2), (4) and (5) can be directly used, but the parameters in the equations need to

be replaced by the parameters of ( ) and ( ).

Because the time is scalar quantity, and isotropic in the complex space, that is time is not related to

the rotary mathematic transformation of the coordinates, therefore , . We get,

( ) (21)

(22)

(

) (23)

Where,

√

(24)

(3) In complex coordinate reference system ( )., is represented by complex distance

with complex angle , rotating clockwise degree, we get coordinate system ( ). In

( ) , is represented by complex distance with complex angle :

And also, |

|, hence,

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（ ) (25)

Because

, therefore,

（

( )） (26)

Substituting equation (17) into equation(26),

( )

Because , therefore,

( )

(27)

Let ( )

(28)

is a real number, and can be called the system time of complex electrodynamic inertial reference

frames. It is not a special time of any particular reference frame, but related to the time of both the

observing system and the observed system. It is the “time” needed to solve some fundamental physic

problems.

To sum up the above discussion, we obtain the basic equations of TCESTR as the following:

(29)

(

) (30)

Where,

√

(31)

( )

(32)

( ) (33)

(34)

Depending on different applications, the above relationship can be further expanded into different

forms.

According to equation (8),

,

. Substituting them into equation (34), we get:

( ) (35)

By substituting equation (32), (33) and (35) into equation (29), we can obtain expanded equations

describing TCESTR with complex speed,

(( ) ) (36)

(

) (37)

Where,

√

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Speed and electric potential has a corresponding relationship. Therefore, we can also obtain another

extended equations describing TCESTR with complex electric potential. This will be discussed later in

the quaternion electrodynamic space-time relativity.

By decomposing (36) into equations of real number and imaginary number, we obtain:

(( ) ) (38)

(( ) ) (39)

Therefore when , then , according to (35) can get , Substituting the

equations into (38)(39)(30) and (31), the special theory of relativity can be obtained:

( )

(

)

√

let , then , according to (35) can get , Substituting the equations into (38)

(39)(30) and (31), a new special theory of relativity can be obtained:

(

) (40)

(41)

(

) (42)

√

(43)

This is the aforementioned the theory of electric potential relativity (TEPR), whose form can be

seen here as symmetric to that of the special theory of relativity, but they have different physical

meaning (will be discussed in another paper).

Part 2. The theory of quaternion electrodynamic space-time relativity (TQESTR)

TCESTR describes relationship between the space-time and the state of complex motion of the

reference frames in the complex plane, but the real axis in the complex plane is one-dimensional. In

reality, our real number space is three-dimensional. Therefore two-dimensional space of TCESTR must

be expanded into four dimensions. In mathematics, the higher form of complex number is quaternion.

Thus TCESTR can be developed into TQESTR. Although the elements of quaternion can have many

variations, they can all be converted uniformly into quaternion velocity or quaternion electric potential.

Their corresponding frame of reference can be called equi-quaternion velocity or equi-quaternion

electric potential frames of reference, or in general be called the quaternion electric inertial frame of

reference.

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Hence, the two basic postulates 5 and 6 of TCESTR can be further expanded into the basic

postulates of TQESTR:

7. Relative principle of quaternion electrodynamic space-time: in any quaternion electrodynamic

inertial reference system, physical laws have the same form;

8. Postulate of quaternion electrodynamic space-time limit: in any quaternion electrodynamic

inertial reference system, the limit of quaternion velocity’s modulus of any point in vacuum is a constant,

; or the limit of quaternion electric potential’s modulus of any point is a constant , .

Where is the speed of light in the vacuum with zero electric potential, and is equal to

. The limit of quaternion electric potential’s modulus only can be determined by

experiment.

According to the basic equation (29) of TCESTR, it can be expanded and separated into real number

equation and imaginary number equation:

(44)

(45)

Notice that equation (45) is a real scalar expression. However, the fact is that the observed

reference frame ( ) moves along the real axis X of the observing reference frame ( )

with vector velocity . Let its unit vector be i , because axes and are the same direction as i.

Multiply both sides of equation (45) by i, equation (45) becomes a vector equation:

(46)

Equations (44) and (46) describe the physical nature more objectively than the complex equation

(29). So the physical quantities about motion will also use vector, such as velocity, displacement and etc.

Equation (46) can be expanded into three-dimensional. If the vector and in equation (46) are

defined as vector and in the three-dimensional space and , corresponding velocity

is defined as , and have the same direction as , and . Let be the unit vectors in the

coordinate of three-dimensional space along the axis , respectively, we have:

(47)

(48)

(49)

becomes . At the same time, let become accordingly. Therefore, equation

(44) and (46) can be transformed into:

(50)

(51)

Equation (50) and (51) form a quaternion space system composed of three real number vectors and

one imaginary number, and is called type quaternion space. This expands the state of motion of the

reference system in the complex plane into motion of the type quaternion space, that is, the reference

system ( ) moves with quaternion velocity relative to the reference frame

( ). Suppose and are quaternion displacement coordinates at any point in the

inertial reference system ( ) and ( ) in the type quaternion space,

respectively, then:

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(52)

The modulus of is , that is √ (53)

(54)

The modulus of is , i.e., √ (55)

Type quaternion velocity and its modulus are:

(56)

√

√

(57)

Where √

Adding equation (50) with (51), and substituting (52), (54) and (56) into it to obtain equation (58).

Also, replacing and of equations (30), (31), (32), (33) and (34)with and ,

the quaternion basic equations can be obtained for TQESTR：

(58)

(

) (59)

where，

√

(60)

(61)

( ) (62)

( )

(63)

Depending on the need, the above basic equation can be transformed into different variations.

Because，

，

，

，then，

( ) (64)

The can also be expressed with quaternions or four-dimensional vector’s dot product.

Hence the quaternion velocity equations can be obtained for TQESTR,

(( ) ) (65)

(

) (66)

Where,

√

(67)

When ， , can be obtained based on equations (52), (54) and

(56), according to equation (64), then ,

(68)

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Therefor the special theory of relativity in any direction ( ) in three-dimensional space can be

obtained [5], [6]

:

(( )

)

(

)

Where,

√

Because imaginary speed and real electric potential are inter-convertible, and real velocity can

be converted into imaginary electric potential vector, hence the quaternion velocity equations can be

converted into another type of quaternion electric potential equations. The quaternion is composed of

one real and three imaginary vectors. It is called H-type quaternion. Through further analysis, both

type quaternion and H-type quaternion are a type of dual quaternion. Rules of operation between the

two dual quaternions are identical to ordinary quaternion [7]

.

Let H-type quaternion electric potential be , then:

( )

( ) (69)

Let

，

，

，

, then:

( )( ) (70)

This shows that H-type quaternion potential is composed of one scalar electric potential and

three imaginary components of the vector electric potential. If the H-type quaternion potential is

divided by speed of light , a new kind of electromagnetic four-dimensional potential . Its physical

significance will be further explored. It is expressed as:

（

， ） (71)

Where, is the electric potential， is the magnetic vector potential.

According to equation (69) from the definition of , we get:

( )

(72)

Because

(73)

Substituting equations (72)(73) into (65)(66)(67) ，the quaternion electric potential equations can

be obtained for TQESTR：

(( )

) (74)

(

) (75)

Where,

√

， (76)

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Part 3. Discussion on the basic effects of the theory of electrodynamic space-time relativity

Although the theory of electrodynamic space-time relativity (TESTR) have various expression

forms, but the forms can all be obtained through conversion and simplification of basic the equations

(58), (59), (60), (61), (62) and (63). Therefore, they will be the main focus for the discussions of the

basic effects of TESTR. The effects are called electrodynamic space-time effect.

1. Superposition principle of TESTR

By analyzing the above equations, one can see that the equations (62) and (59) have the same form as

that of Lorentz transform equations (1) and (4). Therefore, the equations(62)(59) and (60) can also be

written in the form of hyperbolic functions [5]

,

( ) ( ) (77)

( ) ( ) (78)

Where， ( )

√ (

)

(79)

Because， ( ) ( ) (80)

From(79) and(80) it can be obtained： ( )

(81)

Assume： ，

( )

( )

( ) (82)

According to equation(82), the formula for superposition of velocity of TESTR can be obtained：

(83)

Where， √

(84)

√

(85)

When the direction of motion of the reference frame is along the X axis, that is | | ,

, , all other terms are zero. By substituting the above-mentioned formula of

superposition, the formula for velocity superposition of special theory of relativity can be obtained：

(86)

According to the equation (73), the quaternion velocity equations can be converted into quaternion

electric potential equations. Substituting equation (73) into (83), The formula for superposition of

quaternion electric potential of TESTR can be obtained：

(87)

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When the only the scalar electric potential is considered, , , , other

terms are all zero. By substituting the above-mentioned formula, the formula for superposition of scalar

electric potential can be obtained：

(88)

Thus a conclusion that differs from the modern physics is deduced: the superposition of electric

potential is nonlinear. However, if the electric potential is far lower than the electric potential limit，the

equation (88) will change back to linear equation of the current electromagnetics, that is .

2. The time relationship of TESTR

(1) Time effects

In any electrodynamic inertia frame of reference, time is isotropic. The time measured by the clock

put in the real space of the inertial frame is the time of the electrodynamic inertial frame. If two events

happen at two different moments and at the same location of the electrodynamic stationary

inertial reference frame, their time difference is ; for the moments and

corresponding

to the electrodynamic relative inertial reference frame, the time difference is

. From

equations(59), (60) and (57), the equation of quaternion velocity-time change effect of TESTR is:

√

(89)

It shows that the expansion effect of the time is not just about speed, but with potential.

The expression for the quaternion electric potential-time change effect of TESTR is:

√

(90)

In the reference frame of complex electrodynamic inertia, i.e., there are only electric potential and

one dimensional speed , from

, it can be obtained:

√

(91)

In(91), when , the formula for time expansion of special relativity is obtained:

√

(92)

In(91)， , the formula for the time expansion effect of electric potential relativity theory is

obtained:

√

(93)

This is a new important physical effect, called it the potential time expansion effect.

(2) The system time

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The system time is a new concept in TESTR. It unified the observe reference time t and the

observed reference time together. And let basic equations of TESTR become very concise form.

From equations (63), (62) and(59), it can be obtained:

(( )

| | ) (

)

| |

(94)

3. Space change effect of TESTR

In the stationary electrodynamic reference frame , event 1 ( ) and event 2 ( ) occur,

the corresponding events in the moving electrodynamic frames of reference are ( ，

) and

( ，

). is the relative quaternion velocity of two reference frames. From equation (94)，

( ) and (

) can be obtained, therefore from equation (58) it can be known that:

So there is， (95)

(( )

| | ) (

)

| |

(96)

From equation (59), (

) (97)

Let there be an abstract “ruler” in the quaternion space, whose length is obtained through the

measurement of its two end points. In the stationary electrodynamic frame of reference, the ruler is

measured to be , and this measuring process is completed in time . However, in the moving

electrodynamic frame of reference, where the quaternion velocity is , the measuring of its two end

points must simultaneous. Therefore, , and its length is measured to be . Substituting

into equations (96) (97), obtains:

(

)

| | (98)

By substituting(98) into(95), the equation of space change effect of TESTR can be obtained：

| |(

) (99)

Where (100)

Equation (99) is expanded into the equations of imaginary and vector equations of real number：

| |(

) (101)

| |(

) (102)

When ， ，

， , there is：

(103)

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That is, in any space of relative stationary static electric potential, the real space length is not related

to the scalar electric potential. It can be called the real space conservation effect of electric potential.

When ， ，| | ， ，

(104)

This is the formula for length contraction of the special theory of relativity.

4. Predictions and verifications of the theory

The above derivations indicate that in the theory of electrodynamic space-time relativity, time and

space are not only related to velocity but also related to electric potential. Electric potential and velocity

may be interconverted from each other. In principle, different experiments can be designed to verify the

theory. Amongst them, the effect of electric potential time expansion can be more easily tested.

Equation (93) shows that under completely stationary conditions, when there is sufficiently high

electric potential difference between two reference frames, their time difference will also be found. If the

potential is higher, this effect will be more obvious. Therefore, an experiment may be designed: after

calibration, two clocks of high precision Tc and Td are put separately in two identical metallic closed

rooms C and D, which are isolated and motionless relative to each other. Room C is grounded and let its

electric potential be zero. An electric potential generator of super high voltage is used to charge room D

and maintain the super high electric potential comparing to room C. Equation (93) indicates that given

long enough time, after electricity of room D is totally discharged, the electric potential in room D

becomes zero again. Then two clocks Tc and Td are put together to compare their respective reading of

the elapsed time, and . It can be found that there is a time difference between time and

recorded by Tc and Td that is induced by electric potential , and . Comparing the measured

values and the values calculated by equation (93) will verify the theory. If the experiment proves that the

theoretic calculation is correct, then from the experiment data, the magnitude of the electric potential

limit can be obtained by the equation:

√

(105)

It would be extremely difficult to achieve very high electric potential in laboratory. However, the

advantage of this experimental setup is that through adding the experimental time and improving the

accuracy of the time measurement, it lowers the required the electric potential and increases the

possibility of success in the experiment. Base on the theory of electrodyanmic space-time relativity,

many new physical effects can be derived, which in turn, can prove the validity of the theory through

experiments based on the said effects.

This shows the theory of electrodynamic space-time relativity (TESTR) is the generalized name for

the family of relativity theories. Special theory of relativity is a special case of this family. The family

of relativity theories includes the theory of electric potential relativity, the theory of complex relativity,

the theory of quaternion relativity and other combinations and transformations of relativity theories.

These theories of relativity have close relationships, each describing a corresponding space-time.

17 / 17

Space-time is the foundation and core of physics. The theory establishes a new concept, that our space-

time is five dimensional which is composed of quaternion space and time or electrodynamic space-time.

TESTR has a variety of forms of expression. The theory of electricdynamic space-time relativity unites

inertial motion, electromagnetic motion, time and space. Because TESTR predicted some new

electrodynamic space-time effects, some basic theories of physics (such as the Maxwell’s equations and

etc.) will be modified accordingly. They will derive number of new physical effects. These effects will

be rigorously tested through scientific experiments. If future experiments show the theory is correct, its

impact on the physics will be comprehensive and profound. Subsequent papers will further explore

applications and development of the theory.

References：

[1] Einstein, On electrodynamics of moving bodies, Einstein’s Collected Works, Volume 2, Commercial Press, March

1977.

[2] Chen Ximu, Chen Bianqian, Electromagnetic law, establishment and development of the theory of electromagnetic

field, Publishing house of High Education, July 1992, P7-P16

[3] Huang Penghui, Two dimensional special theory of relativity, http://blog.ifeng.com/article/2909546.html , （2009-

07-08）P8-P12

[4] Liu Hua, Brief discussion on derivation and related conversion of the general equation of Lorentz transform, Journal

of Guangxi School of Education, No.3, 2007, P63-64

[5] Shu Xingbei, Special theory of relativity, p49 -51 ISBN 7543613832，Qingdao Press，1995

[6] Su Yanfei, Simple and direct derivation of Lorentz transform, Journal of Zhongshan University, Volum 51, No.5,

October 2001, p183-185,

[7] Fangguan Xu, Quaternion Physics, July 2012, Beijing University Press, page 7